| Summary: | 碩士 === 國立中央大學 === 數學系 === 101 === Surface parameterization is the process of mapping a surface to a planar region. Given any two surfaces with similar topology, it is possible to compute a one-to-one and onto mapping between them. If one of these surfaces is represented by a triangular mesh, the problem of computing such a mapping is referred to as mesh parameterization. The surface that the mesh is mapped to is typically referred to as the parameter domain. The parameterization methods can be roughly classified into fixed boundary methods and free boundary methods. In general, fixed boundary methods are based on the spring model. According to the different choice of weight, results may vary from method to method. In this paper, we parameterize the single boundary meshes with six linear methods by choosing different weight and the non-linear Riemann mapping method. Then we compare the conformality of different methods. Theoretically, the Riemann mapping is an angle-preserving method. On the other hand, the free boundary methods is always consid- ered to minimize energy of the objective function. In our numerical results, Riemann mapping method reaches high efficiency and good conformality. For larger models with 90,000 number of areas, parameterization can be finished within one minute. When several methods address the same parameterization problem, this paper strives to provide an objective comparison between them based on criteria such as parameterization quality, efficiency and robustness.
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